Remark 2.1 
Fixed a finite-dimensional subspace \(E\) , the same argument in [1]} shows that if there is a sequence of injective bounded linear operators \(T_n, n\in \mathbb {N}\)  satisfied that \(T_n\)  converges to \(T\)  on strong operator topology \(SOT(\mathcal {B})\) , then we have \(\det (T_n|_E) \rightarrow \det (T|_E)\)  as \(n\rightarrow \infty \) .

